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DP IB Physics: HL

Revision Notes

Home / IB / Physics: HL / DP / Revision Notes / 6. Circular Motion & Gravitation / 6.1 Circular Motion / 6.1.1 Circular Motion


6.1.1 Circular Motion


Properties of Circular Motion

  • For an object moving in a circle, it will have the following properties:
    • Period
    • Frequency
    • Angular displacement
    • Angular velocity

  • These properties can be inferred from the properties of objects moving in a straight line combined with the geometry of a circle

Motion in a Straight Line

  • When an object moves in a straight line at a constant speed its motion can be described as follows:
    • The object moves at a constant velocity, v
    • Constant velocity means zero acceleration, a
    • Newton's First Law of motion says the object will continue to travel in a straight line at a constant speed unless acted on by another force
    • Newton's Second Law of motion says for zero acceleration that there is no net or resultant force

  • For example, an ice hockey puck moving across a flat frictionless ice rink

6-1-1-moving-puck-no-net-force_sl-physics-rn

An ice puck moving in a straight line

Motion in a Circle

  • If one end of a string was attached to the puck, and the other attached to a fixed point, it would no longer travel in a straight line, it would begin to travel in a circle

6-1-1-motion-in-a-circle_sl-physics-rn

The red arrows represent the velocity vectors of the puck. If the string were cut, the puck would move off in the direction shown by the red vector, as predicted by Newton’s first law.

  • The motion of the puck can now be described as follows:
    • As the puck moves it stretches the string a little to a length r
    • The stretched string applies a force to the puck pulling it so that it moves in a circle of radius r around the fixed point

  • The force acts at 90° to the velocity so there is no force component in the direction of velocity
    • As a result, the magnitude of the velocity is constant
    • However, the direction of the velocity changes

  • As it starts to move in a circle the tension of the string continues to pull the puck at 90° to the velocity
    • The speed does not change, hence, this is called uniform circular motion

6-1-1-puck-with-net-force_sl-physics-rn

The applied force (tension) from the string causes the puck to move with uniform circular motion

Time Period & Frequency

  • If the circle has a radius r, then the distance through which the puck moves as it completes one rotation is equal to the circumference of the circle = 2πr

  • The speed of the puck is therefore equal to:

  • Where:
    • r = the radius of the circle (m)
    • T = the time period (s)

  • This is the same as the time period in waves and simple harmonic motion (SHM)
  • The frequency, f, can be determined from the equation:

Frequency-period equation, downloadable AS & A Level Physics revision notes

Angles in Radians

  • A radian (rad) is defined as:

The angle subtended at the centre of a circle by an arc equal in length to the radius of the circle

6-1-1-one-radian_sl-physics-rn

When the angle is equal to one radian, the length of the arc (S) is equal to the radius (r) of the circle

  • Radians are commonly written in terms of π
  • The angle in radians for a complete circle (360°) is equal to:

Radians Equation 3
  • Use the following equation to convert from degrees to radians:

Radians Equations 5

Table of common degrees to radians conversionsTable of common degrees to radians conversions, downloadable AS & A Level Physics revision notes

Angular Displacement

  • In circular motion, it is more convenient to measure angular displacement in units of radians rather than units of degrees
  • Angular displacement is defined as:

The change in angle, in radians, of a body as it rotates around a circle

  • This can be summarised in equation form:

  • Where:
    • Δθ = angular displacement, or angle of rotation (radians)
    • S = length of the arc, or the distance travelled around the circle (m)
    • r = radius of the circle (m)

  • Note: both distances must be measured in the same units e.g. metres

6-1-1-angle-in-radians_sl-physics-rn

An angle in radians, subtended at the centre of a circle, is the arc length divided by the radius of the circle

Angular Speed

  • Any object rotating with a uniform circular motion has a constant speed but constantly changing velocity
  • Its velocity is changing so it is accelerating
    • But at the same time, it is moving at a constant speed

  • The angular speed, ⍵, of a body in circular motion is defined as:

The rate of change in angular displacement with respect to time

  • Angular speed is a scalar quantity and is measured in rad s–1

 

  • The angular speed does not depend on the length of the line AB
  • The line AB will sweep out an angle of 2π rad in a time T

6-1-1-angular-speed-diagram_sl-physics-rn

The angular speed is ω is the rate at which the line AB rotates

Angular Velocity

  • Angular velocity is a vector quantity and is measured in rad s–1
  • Angular speed is the magnitude of the angular velocity
  • The direction of the angular velocity vector points along the axis of rotation but depends on the direction of rotation

  • The angular velocity vector points in the direction a corkscrew moves when it rotates in the same direction as the circular motion

6-1-1-angular-velocity-vector_sl-physics-rn

Wrap the right hand around the axis of rotation so that the fingers are pointing in the direction of rotation. The thumb points in the direction of the angular velocity vector

Equation Linking Linear & Angular Speed

  • The angular speed and velocity don’t depend on the radius of the circle
  • The linear speed does depend on the radius of the circle

 

6-1-1-linear-and-angular-speed_sl-physics-rn

The angle Δθ is swept out in a time Δt, but the arc lengths s and S are different and so are the linear speeds

  • The linear speed, v, is related to the angular speed, ⍵, by the equation:

v = rω

  • Where:
    • v = linear speed (m s–1)
    • r = radius of circle (m)
    • ⍵ = angular speed (rad s–1)

  • Taking the angular displacement of a complete cycle as 2π, the angular speed ⍵ can be calculated using the equation:

Angular Speed Equation 1

Worked Example

Convert the following angular displacement into degrees:WE - Radians conversion question image, downloadable AS & A Level Physics revision notes

WE - Radians conversion answer image, downloadable AS & A Level Physics revision notes

Worked Example

A bird flies in a horizontal circle with an angular speed of 5.25 rad s−1 of radius 650 m.

Calculate:

  1. The linear speed of the bird
  2. The frequency of the bird flying in a complete circle

WE - Angular speed answer image, downloadable AS & A Level Physics revision notes

Exam Tip

You will notice your calculator has a degree (Deg) and radians (Rad) modeThis is shown by the “D” or “R” highlighted at the top of the screenRemember to make sure it’s in the right mode when using trigonometric functions (sin, cos, tan) depending on whether the answer is required in degrees or radiansIt is extremely common for students to get the wrong answer (and lose marks) because their calculator is in the wrong mode - make sure this doesn’t happen to you!Radians on calculator, downloadable AS & A Level Physics revision notes



  • 1. Measurement & Uncertainties
    • 1.1 Measurements in Physics
      • 1.1.1 SI Units
        • 1.1.2 Using Scientific Notation
          • 1.1.3 Estimating Physical Quantities
          • 1.2 Uncertainties & Errors
            • 1.2.1 Random & Systematic Errors
              • 1.2.2 Calculating Uncertainties
                • 1.2.3 Determining Uncertainties from Graphs
                • 1.3 Vectors & Scalars
                  • 1.3.1 Vector & Scalar Quantities
                    • 1.3.2 Combining & Resolving Vectors
                      • 1.3.3 Solving Vector Problems
                    • 2. Mechanics
                      • 2.1 Motion
                        • 2.1.1 Distance & Displacement
                          • 2.1.2 Speed & Velocity
                            • 2.1.3 Acceleration
                              • 2.1.4 Graphs Describing Motion
                                • 2.1.5 Uniform Acceleration
                                  • 2.1.6 Acceleration of Free Fall Experiment
                                    • 2.1.7 Projectile Motion
                                      • 2.1.8 Terminal Speed
                                      • 2.2 Forces
                                        • 2.2.1 Free-Body Diagrams
                                          • 2.2.2 Newton’s First Law
                                            • 2.2.3 Newton’s Second Law
                                              • 2.2.4 Newton’s Third Law
                                                • 2.2.5 Applying Newton’s Laws of Motion
                                                  • 2.2.6 Friction
                                                  • 2.3 Work, Energy & Power
                                                    • 2.3.1 Kinetic Energy
                                                      • 2.3.2 Gravitational Potential Energy
                                                        • 2.3.3 Elastic Potential Energy
                                                          • 2.3.4 Work Done
                                                            • 2.3.5 Power
                                                              • 2.3.6 Principle of Conservation of Energy
                                                                • 2.3.7 Efficiency
                                                                • 2.4 Momentum & Impulse
                                                                  • 2.4.1 Force & Momentum
                                                                    • 2.4.2 Impulse
                                                                      • 2.4.3 Conservation of Linear Momentum
                                                                        • 2.4.4 Collisions & Explosions
                                                                      • 3. Thermal Physics
                                                                        • 3.1 Thermal Concepts
                                                                          • 3.1.1 Solids, Liquids & Gases
                                                                            • 3.1.2 Temperature
                                                                              • 3.1.3 Internal Energy
                                                                                • 3.1.4 Specific Heat Capacity
                                                                                  • 3.1.5 Specific Latent Heat
                                                                                    • 3.1.6 Phase Change
                                                                                      • 3.1.7 Investigating Thermal Energy
                                                                                      • 3.2 Modelling a Gas
                                                                                        • 3.2.1 Ideal Gas Laws
                                                                                          • 3.2.2 Ideal Gas Equation
                                                                                            • 3.2.3 Kinetic Model of an Ideal Gas
                                                                                              • 3.2.4 Mole Calculations
                                                                                                • 3.2.5 Investigating Gas Laws
                                                                                              • 4. Waves
                                                                                                • 4.1 Oscillations
                                                                                                  • 4.1.1 Properties of Oscillations
                                                                                                    • 4.1.2 Simple Harmonic Oscillations
                                                                                                      • 4.1.3 SHM Graphs
                                                                                                        • 4.1.4 Energy in SHM
                                                                                                        • 4.2 Travelling Waves
                                                                                                          • 4.2.1 Properties of Waves
                                                                                                            • 4.2.2 Transverse & Longitudinal Waves
                                                                                                              • 4.2.3 Electromagnetic Waves
                                                                                                                • 4.2.4 Sound Waves
                                                                                                                • 4.3 Wave Characteristics
                                                                                                                  • 4.3.1 Wavefronts
                                                                                                                    • 4.3.2 Amplitude & Intensity
                                                                                                                      • 4.3.3 Superposition
                                                                                                                        • 4.3.4 Polarisation
                                                                                                                          • 4.3.5 Malus’s Law
                                                                                                                          • 4.4 Wave Behaviour
                                                                                                                            • 4.4.1 Reflection, Refraction & Transmission
                                                                                                                              • 4.4.2 Reflection
                                                                                                                                • 4.4.3 Refraction
                                                                                                                                  • 4.4.4 Determining Refractive Index
                                                                                                                                    • 4.4.5 Single-Slit Diffraction
                                                                                                                                      • 4.4.6 Interference & Path Difference
                                                                                                                                        • 4.4.7 Double-Slit Equation
                                                                                                                                        • 4.5 Standing Waves
                                                                                                                                          • 4.5.1 The Nature of Standing Waves
                                                                                                                                            • 4.5.2 Nodes & Antinodes
                                                                                                                                              • 4.5.3 Boundary Conditions for Standing Waves
                                                                                                                                                • 4.5.4 Harmonics
                                                                                                                                              • 5. Electricity & Magnetism
                                                                                                                                                • 5.1 Electric Fields
                                                                                                                                                  • 5.1.1 Charge & Current
                                                                                                                                                    • 5.1.2 Drift Speed
                                                                                                                                                      • 5.1.3 Potential Difference & DC
                                                                                                                                                        • 5.1.4 Electric Fields
                                                                                                                                                          • 5.1.5 Coulomb’s Law
                                                                                                                                                          • 5.2 Heating Effect of Electric Currents
                                                                                                                                                            • 5.2.1 Circuits
                                                                                                                                                              • 5.2.2 Resistance & Resistors
                                                                                                                                                                • 5.2.3 Kirchhoff’s Circuit Laws
                                                                                                                                                                  • 5.2.4 I-V Characteristics
                                                                                                                                                                    • 5.2.5 Resistivity
                                                                                                                                                                      • 5.2.6 Investigating Resistivity
                                                                                                                                                                        • 5.2.7 Series & Parallel Circuits
                                                                                                                                                                          • 5.2.8 Heating Effect of Current
                                                                                                                                                                            • 5.2.9 Potential Divider Circuits
                                                                                                                                                                            • 5.3 Electric Cells
                                                                                                                                                                              • 5.3.1 Primary & Secondary Cells
                                                                                                                                                                                • 5.3.2 Investigating Electric Cells
                                                                                                                                                                                  • 5.3.3 Terminal Potential Difference
                                                                                                                                                                                    • 5.3.4 Electromotive Force & Internal Resistance
                                                                                                                                                                                    • 5.4 Magnetic Effects of Electric Currents
                                                                                                                                                                                      • 5.4.1 Magnetic Fields
                                                                                                                                                                                        • 5.4.2 Magnetic Force on a Charge
                                                                                                                                                                                          • 5.4.3 Magnetic Force on a Current-Carrying Conductor
                                                                                                                                                                                            • 5.4.4 Solving Problems Involving Magnetic Forces
                                                                                                                                                                                          • 6. Circular Motion & Gravitation
                                                                                                                                                                                            • 6.1 Circular Motion
                                                                                                                                                                                              • 6.1.1 Circular Motion
                                                                                                                                                                                                • 6.1.2 Centripetal Force
                                                                                                                                                                                                  • 6.1.3 Centripetal Acceleration
                                                                                                                                                                                                    • 6.1.4 Applications of Circular Motion
                                                                                                                                                                                                    • 6.2 Newton’s Law of Gravitation
                                                                                                                                                                                                      • 6.2.1 Newton’s Law of Gravitation
                                                                                                                                                                                                        • 6.2.2 Circular Orbits
                                                                                                                                                                                                          • 6.2.3 Gravitational Field Strength
                                                                                                                                                                                                        • 7. Atomic, Nuclear & Particle Physics
                                                                                                                                                                                                          • 7.1 Discrete Energy & Radioactivity
                                                                                                                                                                                                            • 7.1.1 Discrete Energy Levels
                                                                                                                                                                                                              • 7.1.2 Calculating Discrete Energies
                                                                                                                                                                                                                • 7.1.3 Emission & Absorption Spectrum
                                                                                                                                                                                                                  • 7.1.4 Isotopes & Radioactive Decay
                                                                                                                                                                                                                    • 7.1.5 Background Radiation
                                                                                                                                                                                                                      • 7.1.6 Alpha, Beta & Gamma Particles
                                                                                                                                                                                                                        • 7.1.7 Decay Equations
                                                                                                                                                                                                                          • 7.1.8 Half-Life
                                                                                                                                                                                                                            • 7.1.9 Investigating Half-Life
                                                                                                                                                                                                                            • 7.2 Nuclear Reactions
                                                                                                                                                                                                                              • 7.2.1 Atomic Mass Unit
                                                                                                                                                                                                                                • 7.2.2 Mass Defect & Nuclear Binding Energy
                                                                                                                                                                                                                                  • 7.2.3 Nuclear Fission & Fusion
                                                                                                                                                                                                                                    • 7.2.4 Binding Energy per Nucleon Curve
                                                                                                                                                                                                                                    • 7.3 The Structure of Matter
                                                                                                                                                                                                                                      • 7.3.1 Discovery of the Nucleus
                                                                                                                                                                                                                                        • 7.3.2 Quarks & Leptons
                                                                                                                                                                                                                                          • 7.3.3 Hadrons, Baryons & Mesons
                                                                                                                                                                                                                                            • 7.3.4 Particle Conservation Laws
                                                                                                                                                                                                                                              • 7.3.5 Fundamental Forces
                                                                                                                                                                                                                                                • 7.3.6 Feynman Diagrams & Confinement
                                                                                                                                                                                                                                                  • 7.3.7 The Standard Model of Particle Physics
                                                                                                                                                                                                                                                • 8. Energy Production
                                                                                                                                                                                                                                                  • 8.1 Energy Sources
                                                                                                                                                                                                                                                    • 8.1.1 Specific Energy
                                                                                                                                                                                                                                                      • 8.1.2 Sankey Diagrams
                                                                                                                                                                                                                                                        • 8.1.3 Primary & Secondary Energy Sources
                                                                                                                                                                                                                                                          • 8.1.4 Energy Resources
                                                                                                                                                                                                                                                            • 8.1.5 Energy Generation
                                                                                                                                                                                                                                                              • 8.1.6 Safety Issues in Nuclear Power
                                                                                                                                                                                                                                                              • 8.2 Thermal Energy Transfer
                                                                                                                                                                                                                                                                • 8.2.1 Conduction, Convection & Thermal Radiation
                                                                                                                                                                                                                                                                  • 8.2.2 Black-Body Radiation
                                                                                                                                                                                                                                                                    • 8.2.3 The Solar Constant, Albedo & Emissivity
                                                                                                                                                                                                                                                                      • 8.2.4 The Greenhouse Effect
                                                                                                                                                                                                                                                                        • 8.2.5 Earth's Surface–Atmosphere System
                                                                                                                                                                                                                                                                      • 9. Wave Phenomena (HL only)
                                                                                                                                                                                                                                                                        • 9.1 Simple Harmonic Motion
                                                                                                                                                                                                                                                                          • 9.1.1 The Defining Equation of SHM
                                                                                                                                                                                                                                                                            • 9.1.2 Energy Changes in SHM
                                                                                                                                                                                                                                                                              • 9.1.3 Calculating Energy Changes in SHM
                                                                                                                                                                                                                                                                                • 9.1.4 Examples of SHM
                                                                                                                                                                                                                                                                                • 9.2 Single-Slit Diffraction
                                                                                                                                                                                                                                                                                  • 9.2.1 The Nature of Single-Slit Diffraction
                                                                                                                                                                                                                                                                                    • 9.2.2 Intensity of Interference Maxima & Minima
                                                                                                                                                                                                                                                                                    • 9.3 Interference
                                                                                                                                                                                                                                                                                      • 9.3.1 Young’s Double-Slit Experiment
                                                                                                                                                                                                                                                                                        • 9.3.2 Two-Slit Interference Patterns
                                                                                                                                                                                                                                                                                          • 9.3.3 Diffraction Grating Patterns
                                                                                                                                                                                                                                                                                            • 9.3.4 The Diffraction Grating Equation
                                                                                                                                                                                                                                                                                              • 9.3.5 Thin Film Interference
                                                                                                                                                                                                                                                                                              • 9.4 Resolution
                                                                                                                                                                                                                                                                                                • 9.4.1 The Rayleigh Criterion
                                                                                                                                                                                                                                                                                                  • 9.4.2 Rayleigh Criterion Calculations
                                                                                                                                                                                                                                                                                                    • 9.4.3 Resolvance of Diffraction Gratings
                                                                                                                                                                                                                                                                                                    • 9.5 Doppler Effect
                                                                                                                                                                                                                                                                                                      • 9.5.1 The Doppler Effect
                                                                                                                                                                                                                                                                                                        • 9.5.2 Uses of The Doppler Effect
                                                                                                                                                                                                                                                                                                          • 9.5.3 The Doppler Equation
                                                                                                                                                                                                                                                                                                        • 10. Fields (HL only)
                                                                                                                                                                                                                                                                                                          • 10.1 Describing Fields
                                                                                                                                                                                                                                                                                                            • 10.1.1 Gravitational & Electrostatic Fields
                                                                                                                                                                                                                                                                                                              • 10.1.2 Gravitational & Electrostatic Field Lines
                                                                                                                                                                                                                                                                                                                • 10.1.3 Gravitational & Electrostatic Potential
                                                                                                                                                                                                                                                                                                                  • 10.1.4 Equipotential Surfaces
                                                                                                                                                                                                                                                                                                                  • 10.2 Fields at Work
                                                                                                                                                                                                                                                                                                                    • 10.2.1 Potential & Potential Energy
                                                                                                                                                                                                                                                                                                                      • 10.2.2 Potential Energy Calculations
                                                                                                                                                                                                                                                                                                                        • 10.2.3 Potential Gradient & Difference
                                                                                                                                                                                                                                                                                                                          • 10.2.4 Potential in a Charged Sphere
                                                                                                                                                                                                                                                                                                                            • 10.2.5 Escape Speed
                                                                                                                                                                                                                                                                                                                              • 10.2.6 Orbital Motion, Speed & Energy
                                                                                                                                                                                                                                                                                                                                • 10.2.7 Forces & Inverse-Square Law Behaviour
                                                                                                                                                                                                                                                                                                                                  • 10.2.8 Forces on Charges & Masses
                                                                                                                                                                                                                                                                                                                                • 11. Electromagnetic Induction (HL only)
                                                                                                                                                                                                                                                                                                                                  • 11.1 Electromagnetic Induction
                                                                                                                                                                                                                                                                                                                                    • 11.1.1 Emf, Magnetic Flux & Magnetic Flux Linkage
                                                                                                                                                                                                                                                                                                                                      • 11.1.2 Induced Emf
                                                                                                                                                                                                                                                                                                                                        • 11.1.3 Faraday’s Law
                                                                                                                                                                                                                                                                                                                                          • 11.1.4 Lenz’s Law
                                                                                                                                                                                                                                                                                                                                          • 11.2 Power Generation & Transmission
                                                                                                                                                                                                                                                                                                                                            • 11.2.1 AC Generators
                                                                                                                                                                                                                                                                                                                                              • 11.2.2 Root-Mean-Square Current & Voltage
                                                                                                                                                                                                                                                                                                                                                • 11.2.3 Step-Up & Step-Down Transformers
                                                                                                                                                                                                                                                                                                                                                  • 11.2.4 Transformer Calculations
                                                                                                                                                                                                                                                                                                                                                    • 11.2.5 AC Electrical Power Distribution
                                                                                                                                                                                                                                                                                                                                                      • 11.2.6 Diode Bridges
                                                                                                                                                                                                                                                                                                                                                        • 11.2.7 Investigating Diode Bridges
                                                                                                                                                                                                                                                                                                                                                          • 11.2.8 Rectification
                                                                                                                                                                                                                                                                                                                                                            • 11.2.9 Capacitors & Diode Bridges
                                                                                                                                                                                                                                                                                                                                                            • 11.3 Capacitance
                                                                                                                                                                                                                                                                                                                                                              • 11.3.1 Capacitance
                                                                                                                                                                                                                                                                                                                                                                • 11.3.2 Dielectric Materials
                                                                                                                                                                                                                                                                                                                                                                  • 11.3.3 Capacitors in Series & Parallel
                                                                                                                                                                                                                                                                                                                                                                    • 11.3.4 The Time Constant
                                                                                                                                                                                                                                                                                                                                                                      • 11.3.5 Energy Stored in a Capacitor
                                                                                                                                                                                                                                                                                                                                                                        • 11.3.6 Capacitor Charge & Discharge
                                                                                                                                                                                                                                                                                                                                                                          • 11.3.7 Discharge Calculations
                                                                                                                                                                                                                                                                                                                                                                        • 12. Quantum & Nuclear Physics (HL only)
                                                                                                                                                                                                                                                                                                                                                                          • 12.1 The Interaction of Matter with Radiation
                                                                                                                                                                                                                                                                                                                                                                            • 12.1.1 Photons
                                                                                                                                                                                                                                                                                                                                                                              • 12.1.2 The Photoelectric Effect
                                                                                                                                                                                                                                                                                                                                                                                • 12.1.3 Observing the Photoelectric Effect
                                                                                                                                                                                                                                                                                                                                                                                  • 12.1.4 Solving Photoelectric Problems
                                                                                                                                                                                                                                                                                                                                                                                    • 12.1.5 Matter Waves
                                                                                                                                                                                                                                                                                                                                                                                      • 12.1.6 Pair Production & Annihilation
                                                                                                                                                                                                                                                                                                                                                                                        • 12.1.7 Quantization of Angular Momentum
                                                                                                                                                                                                                                                                                                                                                                                          • 12.1.8 The Wave Function
                                                                                                                                                                                                                                                                                                                                                                                            • 12.1.9 The Uncertainty Principle
                                                                                                                                                                                                                                                                                                                                                                                              • 12.1.10 Tunnelling
                                                                                                                                                                                                                                                                                                                                                                                              • 12.2 Nuclear Physics
                                                                                                                                                                                                                                                                                                                                                                                                • 12.2.1 Rutherford Scattering & Nuclear Radius
                                                                                                                                                                                                                                                                                                                                                                                                  • 12.2.2 Nuclear Scattering
                                                                                                                                                                                                                                                                                                                                                                                                    • 12.2.3 Deviations from Rutherford Scattering
                                                                                                                                                                                                                                                                                                                                                                                                      • 12.2.4 Nuclear Energy Levels
                                                                                                                                                                                                                                                                                                                                                                                                        • 12.2.5 The Neutrino
                                                                                                                                                                                                                                                                                                                                                                                                          • 12.2.6 The Law of Radioactive Decay
                                                                                                                                                                                                                                                                                                                                                                                                            • 12.2.7 Measuring Half-Life
                                                                                                                                                                                                                                                                                                                                                                                                          Katie Moon

                                                                                                                                                                                                                                                                                                                                                                                                          Author: Katie

                                                                                                                                                                                                                                                                                                                                                                                                          Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.


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